一类拟对称微分自治系统的广义中心与极限环分支
General Center Conditions and Bifurcation of Limit Cycles for a Quasi-symmetric Polynomial System
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摘要: 研究一类平面拟对称微分自治系统,通过2个适当的变换以及广义焦点量的仔细计算,得出了该系统的无穷远点与初等焦点能够同时成为广义中心的条件,进一步得出在一定条件下该系统能够分支出10个极限环的结论,其中5个大振幅极限环来自无穷远点,5个小振幅极限环来自初等焦点.Abstract: A class of quasi-symmetric seventh degree system was studied.By making two appropriate transformations and general focal values calculation,the conditions that the infinity and the elementary focus become general centers at the same time are obtained.Furthermore,10 limit cycles including 5 small limit cycles from the elementary focus and 5 large limit cycles from the infinity can occur under a certain condition.
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